We present a fully parallel attack against ECMQV and ECHMQV–C, the elliptic curve variants of the MQV and HMQV–C protocols. When m processors are used and ECMQV is instantiated over a group of order n, our attack runs in time \(\mathcal {O}(\sqrt{n}/m)\) ; it requires no shared storage and is more efficient than the parallel Pollard’s rho algorithm. For the ECHMQV–C protocol, when the aim is to impersonate some party \(\hat{A}\) to any party among \(\hat{B}_1, \hat{B}_2, \cdots , \hat{B}_z\) , the expected running time of our attack is \(\mathcal {O}(\sqrt{n}/(zm))\) .